The Cartesian Semantics of the Port Royal Logic

John N. Martin

• Publisher: Routledge
• Year: 2019
• Print ISBN:
  9781032337708
• eBook ISBN:
  9781351249171
• Topic: Philosophy
• Subtopic: Modern Philosophy

This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l'Art de penser, 1662-1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes' metaphysics. The Logic's authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book's central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea's defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic's metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.

1 The Semantics of Terms. Intentional Content

A Cartesian Challenge

Arnauld and Nicole inherited and sustained an immense logical tradition. As followers of Descartes, they rejected some of Aristotle’s views, but with respect to much of earlier logic they were conservative. Although they de-emphasis scholastic material like the syllogistic and placed new emphasize on others like intentional content, they endorsed unchanged large parts of medieval logic. A major exception was the theory of reference or, as they called it, signification. Signification lay at the heat of the earlier logical tradition because it entered into the definition of many other ideas. The standard explanation of signification, however, which held that bodily modes travels to the soul, was undermined by dualism. The reconstruction of signification is set out in Part I of the Logic. This chapter describes how the account is built up out of two parts: standard distinctions from traditional logic plus a reworked concept of intentional content based on the medieval notion of objective being.

Cartesian Ontology

At several points the Logic’s the authors refuse to engage in metaphysics, which they regarded as a fruitless endeavor. They set aside as useless the problem of universals—the issue of whether universals exist, as they put it, a parte rei.¹ They also dismiss as “inconceivable” various Aristotelian concepts like substantial form, weight, and attractive powers.² Instead, they endorse Descartes’ dualism and his quasi-geometric physics of extended matter. But their remarks that distance themselves from Aristotle are misleading. Their rebellion was selectively. Key to their distinctive views is a long list of Aristotelian concepts that had become orthodox in medieval logic.

1LAP, Discours I, KM V 112–113, B 11–12.

2LAP IV.6, KM V 380–381, B 249.

Perhaps their most fundamental Aristotelian commitment is to a substance-mode ontology. Part I endorses a long list of Aristotelian concepts that detail this ontology, which may be summarized here. The authors begin by partitioning Being into its two broadest species: substances and modes. This partitions is subdivided in the traditional way into Aristotle’s ten categories: substance and nine species of modes: quality, quantity, relation, activity, passivity, place, time, position, and state.³ Modes are also called attributes and qualities. The distinction between substances and modes is explained in the orthodox way. Substances have independent existence, but modes exist only as instantiated in substances. Modes are cross-classified into Porphyry’s five predicables: genus, species, difference, property (proprium), and accident.⁴ Predicables are distinguished from one another by the degree to which a mode is instantiated necessarily. Every species and genus has a necessary nature, whereas properties are necessary but not definitive, and accidents are contingent.

3LAP I.3, KM V 137–138, B 33–34. The authors describe the distinctions among the nice varieties of modes as “fairly useless.” With the exception of relations, they seldom refer to them.

4LAP I.7, KM V 146–150, B 40–44.

A species’ nature or essence is described in a real definition, which is a necessarily true proposition that affirms of the species its genus and difference. As a result of their natures, species fall into a finitely branching finite tree-hierarchy that is headed by the highest genus, Being. Scientific knowledge consists primarily of essential definitions and their consequences.⁵ All of these are thoroughly orthodox Aristotelian views. We shall see, however, that the authors give them a distinctive Cartesian cast.

5LAP I.6, 7, and 12.

The Logic’s main departure from Aristotelian ontology is its dualism. The category of substance, it claims, is partitioned into “mind and body.” These “are the two species of substance.”⁶ Although most medieval logicians would concur that there exists a fundamental difference between spiritual and material substance, what is distinctive in the Logic is the additional principle that the two species of substance cannot share modes. Modes that inhere in minds cannot inhere in bodies, and material modes cannot inhere in spirits. Although the principle has a ring of plausibility given dualism—indeed one wonders why ancient ontologists were not more troubled about spirits and minds sharing properties—it has devastating implications for the foundations of medieval metalogic. The inability of material modes to affect the mind vitiates what was then the standard account of signification, and along with signification other parts of the theory which were defied in terms of signification, for example, the definitions of truth and validity.

6LAP I.6, KM V 148, B 42.

The standard theory had turned on the premise that material modes travel to the soul. As logic developed in the 13th century, it became accepted that, in the first instance, language is mental. Ontologically, language was believed to consist of accidental modes of the soul or “mental acts.” These were thought to have a structure or grammar. Basic mental acts, which were called concepts, were understood to be signs for things in the world, or to be “significative.” They could represent any category of being, whether material and spiritual. Concepts in turn were parts of, or causal preliminaries to, more complex acts called propositions. Propositions took various grammatical forms. Of these the four categorical propositions of the syllogistic were basic. Concepts served as their terms. A proposition was true or false depending on whether the world was “as its terms signified.” A series of ordered propositions, in turn, formed a yet more complex structure called an arguments. An argument was valid or invalid depending on whether its inference preserved truth. There was an immense logical lore spelling out the details. It was not the purpose of the Port Royal Logic to overthrow this body of theory. The Logic is more accurately described as reworking elementary parts of medieval logic in a way that made it consistent with Descartes’ philosophy. Providing a new analysis of signification was a major challenge.

Medieval Theories of Signification

Theories varied, but Aquinas’ account of signification is representative. As a true Aristotelian, Aquinas understood concept formation to be empirical: “there is nothing in the intellect that was not first in the senses.”⁷ He conceived sensation to start with a physical process in which sensible properties, called a “sensible species,” are conveyed through a sensible medium, like air and the sense organs, to be ultimately instantiated in the brain. Once the properties leave the body, they were thought to have a special ontological property: they did not affect—they were not “true of”—the medium in which they were instantiated. When a rose is seen, its redness travels through the air to the eyes without making either the air or the eyes red. A property in this state was said to be “intentional” in the sense that although it is instantiated in a subject, it is not true of the subject. The property is then conveyed from the body to the soul by the passive faculty of imagination, through which the soul experiences what Aquinas called a “phantasm,” a state of awareness of the properties of the individual being sensed. This set of properties was called the perceived individual’s “sensible species.” In Aquinas’ view the very properties previously instantiated in the body outside the mind were instantiated in the soul but in what he called an “immaterial” and “immobile” way. It is this transfer of properties from the body to the soul that Arnauld and Nicole rejected. For dualists, a material property cannot be instantiated in the soul even “intentionally.”

7For Aquinas see Summa theologiae 1.1a, qq. 84 and 85, specifically q. 84, aa. 1, 2, 6, and 7, and q. 85, a. 1. The quotation is from De veritate, q. 2, a. 3, arg. 19. Thomas Aquinas 2006 [1970]: Nihil est in intellectu quod non sit prius in sensu.

According to Aquinas, imagination is an intermediate stage of concept formation. Imagination is followed by “abstraction.” From the panoply of the individual’s particular properties experienced as part of the phantasm, the active intellect separates out one or more properties. The selected properties are then instantiated as a unit separately in the soul, again in an intentional manner. The actualization of this separate property instantiation is a mental act called a “concept,” the ancestor of what the Cartesians would later call an idea.

Aquinas’ causal process requires both the phantasm, as a “material cause,” and the agent intellect, called an “active cause” because it acts upon the material cause to form a concept. Aquinas also holds, somewhat mysteriously, that the intellect may abstract from the sensible species the properties that constitute object’s essential nature—its “quiddity” or “intelligible species”—which he says is generally non-sensible or “invisible.”⁸

8For more detailed accounts along the same line see Ockham, Reportatio II, q. 13 in William of Ockham 1981; John Buridan, Commentary on Aristotle’s De Anima II, q. 9, Chapt. 35, in John Buridan 1984, pp. 495–512, and Questions on Aristotle’s De Anima, q. 8, in John Buridan 1989, pp. 288–311.

The doctrine of sensation and abstraction is directly relevant to medieval semantics because the process is supposed to explain why concepts are “significative.” The concept, which is a property instantiated in the soul, is the same property that was that was formerly instantiated in an individual outside the mind. The property in the soul, albeit instantiated intentionally, is supposed to be numerically identical to the property instantiated in object outside the mind. Nominalists, who denied that numerically the same property can be instantiated in more than one individual, would say that the property-instance in the soul is “similar” to the instance in the individual. In either case, the property in the soul, the so-called concept, possesses signification in two ways: descriptively and causally. Descriptively, it signifies all individuals that possess that property or, if you are a nominalist, it signifies all individuals that instantiate similar property-instances. Causally, it signifies all individuals that could have caused a phantasm from which the property concept could have been abstracted. In the passage below Aquinas refers to both the descriptive and causal properties of the concept, and speaks of the relation of the concept to its cause as one of similarity (aedequatio):⁹

9De veritate, Thomas Aquinas 2006 [1970] [51577] q. 1, a. 1, arg. 7:

Convenientiam vero entis ad intellectum exprimit hoc nomen verum. Omnis autem cognitio perficitur per assimilationem cognoscentis ad rem cognitam, ita quod assimilatio dicta est causa cognitionis: sicut visus per hoc quod disponitur secundum speciem coloris, cognoscit colorem. Prima ergo comparatio entis ad intellectum est ut ens intellectui concordet: quae quidem concordia adaequatio intellectus et rei dicitur; et in hoc formaliter ratio veri perficitur. Hoc est ergo quod addit verum super ens, scilicet conformitatem, sive adaequationem rei et intellectus; ad quam conformitatem, ut dictum est, sequitur cognitio rei. Sic ergo entitas rei praecedit rationem veritatis, sed cognitio est quidam veritatis effectus. Secundum hoc ergo veritas sive verum tripliciter invenitur diffiniri. ...

Table of contents

• Cover
• Half Title
• Series
• Title
• Copyright
• Dedication
• Contents
• Acknowledgments
• Abbreviations
• Introduction
• 1 The Semantics of Terms. Intentional Content
• 2 The Semantics of Terms. Signification and Extension
• 3 The Semantic of Terms. The Structure of Ideas
• 4 The Semantics of Propositions. Truth and Consequences
• 5 The Semantics of Discourse. Method
• 6 The Semantics of Discourse. Existential Import
• Appendix
• Index